Magnetostriction Loops Research Articles

Magnetostriction property modeling of silicon steel considering stress-induced and magnetocrystalline anisotropy

This paper proposed an improved magnetostriction model for correlation of anisotropy in non-oriented (NO) silicon steel based on the free energy, which considers stress-induced and magnetocrystalline anisotropy. Firstly, the free energy model, which includes stress-induced anisotropy energy, the energy of magnetic field, and the anisotropic energy of magnetic crystals, is incorporated into the anhysteretic magnetization parameter Man. Then, to obtain the magnetic field and proposed model parameters related to stress-induced and magnetocrystalline anisotropy, the magnetostrictive strain loops at different magnetization directions of NO silicon steel are measured. Finally, based on the parameters obtained from experimental data of the proposed model, magnetostrictive strain loops under varying magnetization directions are simulated. This improved magnetostriction model can be applied to the calculation of the vector magnetostriction of the motor core.

The emergence of high room temperature in-plane and out-of-plane magnetostriction in polycrystalline CoFe2O4 film

The polycrystalline CoFe2O4 (CFO) film on cantilever substrate of silicon was grown using pulsed laser deposition (PLD) method and investigated its in-plane and out-of-plane magnetostrictive strain at room temperature (300 K) using the indigenous optical Cantilever Beam Magnetometer (CBM). The film shows a high compressive magnetostrictive strain of ‒ 387 ppm and ‒ 708 ppm for in-plane and out-of-plane configurations, respectively. Considerably, the magnetostrictive strain loops (λ‒H) possess a certain degree of hysteresis with a symmetric butterfly shape. The origin of large compressive magnetostriction of CFO film is attributed to the non-180° domain wall motion followed by 90° domain rotation. The large values of saturation magnetostrictive strain make CFO film a suitable candidate in sensor design for different purposes.

An improved magnetostriction model of silicon steel considering the saturated magnetic domain wall movement

To obtain the deformation characteristic of silicon steel with yoke clamping applied under an alternating magnetic field, a stress-dependent magnetostriction model of silicon steel must be constructed. Due to the magnetic domain’s rotation and the magnetic domain wall movement with stress applied, the material’s magnetostrictive deformation will reverse and saturate in both magnitude and direction. Therefore, the saturated magnetic domain wall movement effect must be considered in the stress-dependent magnetostriction model. Firstly, a hysteresis stress-dependent magnetostriction model based on the Jiles-Atherton (J-A) model and Zheng-Liu (Z-L) model is proposed. Then, the magnetostrictive deformation curves of the non-oriented silicon steel with external stresses are measured. The magnetic field and deformation parameters that control the saturated magnetic domain wall movement are extracted and applied to the model. Finally, the magnetostrictive loops with the magnetic field under varying stress are obtained based on the proposed model. The proposed model’s effectiveness and accuracy are verified by comparing the measurement results with the simulation results.

Phase-field simulation of magnetic microstructure and domain switching in (Tb0.27Dy0.73)Fe2 single crystal

The morphotropic phase boundary (MPB), separating two ferroic phases with rhombohedral and tetragonal crystal symmetries, has been utilized extensively in ferroelectrics because it can lead to high-performance piezoelectricity. Recently, a parallel ferromagnetic MPB was experimentally reported and was suggested that the optimal point for magneto-mechanical applications might lies on the rhombohedral side. However, the insight of the domain structures and switching mechanism near ferromagnetic MPB is still unclear. In this work, phase-field micromagnetic microelastic modeling was employed to simulate the domain formation and magnetization switching of (Tb0.27Dy0.73)Fe2, whose composition is around the rhombohedral side of ferromagnetic MPB. The results show that four kinds of domains of the rhombohedral phase automatically form twins of {110} or {100} boundaries with 71° and 109° domain walls after a process of nucleation and growth. The rhombohedral domain evolution and phase volume fraction under the external field of 120 kA/m along different directions are investigated. In ferromagnetics subject to an alternating magnetic field, domain magnetization switches to cause a magnetization hysteresis loop and an associated butterfly magnetostriction loop with the alternating magnetic field.

Bipolar magnetostriction in CoFe2O4: Effect of sintering, measurement temperature, and prestress

Magnetostrictive materials are potential candidates for many applications such as sensors, actuators, transducers, and other magnetoelectric applications. Cobalt ferrite (CoFe2O4) has proven to be favorable in comparison with commonly used magnetostrictive materials due to its high magnetostriction coefficient and low cost. This work deals with the synthesis of CoFe2O4 and subsequent characterization of its magnetostrictive properties. Hydrothermal route was adopted for the synthesis, and the effect of sintering and measurement temperatures on the magnetostrictive response of the synthesized samples was also established. Bipolar magnetostriction has been observed in pure CoFe2O4 for the first time, and its control by means of the sintering temperature has been elucidated. The results thus reveal that the temperature is an important parameter in determining the magnetostrictive characteristics of CoFe2O4. The switching from bipolar to unipolar magnetostriction under elevated sintering and measurement temperatures was also observed, and this was owed to the crystal anisotropy of the material. The effect of prestress on the magnetostriction was also studied, wherein it was observed that the application of a compressive prestress resulted in broadening of the magnetostriction loops. The reported bipolar magnetostrictive characteristics are quite interesting and hence can prove to be cost-effective in comparison with existing magnetostrictive materials.

An Improved Magnetostriction Model for Electrical Steel Sheet Based on Jiles–Atherton Model

The magnetostriction of an electrical steel sheet (ESS) is the main cause of the electromagnetically induced vibration of power transformers. In order to analyze the magnetostrictive hysteresis property of an ESS, a model is established based on the improved Jiles-Atherton (J-A) model by introducing the parameter k 1 , which considers the domain moment rotation. The magnetostrictive hysteretic loop of silicon steel would be obtained by combining the hysteretic loop with the model, in which the hysteretic loops can be more easily measured accurately than the magnetostriction loops. To verify the feasibility of the model, it is applied to Grain-oriented and non-oriented electrical steel, and the parameters in the model are extracted by using a particle swarm optimization algorithm. By comparing the measured data to calculate data obtained from the model, excellent agreement in the result is shown. The anisotropic properties of non-oriented silicon steel are also suitably shown. The results demonstrate the proposed model in the article is accurate for dynamic magnetic characteristics to electrical steel. It provides a good description of magnetostriction under the magnetic field with different amplitudes.

Unified First Order Inertial Element Based Model of Magnetostrictive Hysteresis and Lift-Off Phenomenon.

The present paper presents a new model of magnetostrictive hysteresis loop. A unified approach of both the hysteresis of λ(B) relation, as well as the lift-off phenomenon is proposed, which are explained together on the base of the response of the first order inertial element. Considering previously presented reports, the Maxwell–Boltzmann distribution based model of magnetostrictive characteristics with local maxima, enables modeling magnetostrictive loops. The model was validated on the results of measurements of magnetostrictive hysteresis loops of Mn0.70Zn0.24Fe2.06O4 ferrite for power applications. Good agreement was confirmed for major magnetostrictive loop, especially for smaller values of flux density. As a result, the proposed model may be used for modeling the magnetostrictive response of inductive components of electrical machines, power conversion devices or magnetostrictive actuators.

Effect of Magnetic Inclusions on the Effective Magnetostriction of Bulk Superconductors

A simple model is presented based on the Kim–Anderson model to further investigate the dependence of the effective magnetostriction of magnetic inclusion-superconducting matrix system on both the elastic and magnetic parameters including the elastic modulus, permeability, and volume fraction. The effect of the permeability on the magnetostriction is also obtained by implementing the continuity conditions of displacement and strain at the interface between the inclusion and the matrix through the magnetostriction loop. The results indicate that a stiffer inclusion can decrease the effective magnetostriction no matter whether the inclusion is magnetic or not and a larger effective magnetostriction can be obtained by choosing the matrix with a higher permeability, which gives an explanation about why the composite made from a matrix with a high permeability but a negligibly small magnetostriction yields unexpectedly low magnetostriction. Of particular interest is that in a certain range the effective magnetostriction of composites can be enhanced until it is saturated by increasing the permeability of matrix.

3D Modeling Effect of Spherical Inclusions on the Magnetostriction of Bulk Superconductors

In this paper, the dependence of the effective magnetostriction of bulk superconductors on the elastic parameters including the volume fraction and elastic modulus ratio is studied by a three-dimensional model consisting of a spherical inclusion–superconducting matrix system. The effect of the elastic modulus and volume fraction on the magnetostriction is also obtained through the magnetostriction loop. The results indicate that the elastic modulus and volume fraction have obvious effects on the effective magnetostriction of the superconducting composite, which gives an explanation about the differences between the experimental and the theoretical results. Furthermore, it is worth pointing out that the linear field dependence of magnetostriction is unique to the Bean model by comparing the curve shapes of the magnetostriction loop with and without inclusion.

Suppression of nonlinear magnetoelectric effect hysteresis in a layered ferromagnetic-piezoelectric structure

Nonlinear magnetoelectric effect in a planar ferromagnetic-piezoelectric composite structure, placed in the constant magnetic field H and harmonic alternating field h, manifests itself in voltage harmonics generation. The hysteresis in the field dependence of magnetostriction of the ferromagnetic layer leads to an ambiguous dependence of the harmonic amplitudes on H. The effect of the hysteresis suppression in the harmonic amplitudes dependences on the field H under increasing amplitude of the excitation field is described in the paper. In a planar structure with Ni and lead zirconate titanate layers, an increase in the field h from 1Oe to 100Oe led to a decrease of the coercive field from 21Oe to 0.4Oe in the field dependence of the first and third voltage harmonics amplitudes. The simulation showed that the effect is caused by a decrease in the relative influence of the constant field on the asymmetry of the ferromagnetic layer magnetostriction loop of the structure with increase of the excitation field. The hysteresis suppression effect will increase the measurement accuracy of the magnetoelectric sensors.

On the Measurement of Permeability and Magnetostriction in Ribbons and Wires

The magnetostrictive delay line (MDL) principle is used to evaluate the magnetic and magnetostrictive properties of materials with waveguide-like shape, such as ribbons and wires. The material under test is used as the MDL on which a pulsed field along with a dc bias field is applied at the excitation point while another dc bias field is applied at the receiving end. Theoretical analysis shows that varying the dc bias field at the receiving end while keeping the excitation field constant results in the dc differential permeability measurement, the integral of which yields the dc hysteresis loop of the material, i.e., B(H). The response obtained upon varying the dc bias field at the excitation point, while keeping all else constant, is proportional to the derivative with respect to field of the dc magnetostriction loop, i.e., λ(H). The theoretical analysis is supported by experimental results obtained on FeSiB wires and ribbons.

Critical state model for magneto-elastic problem of thin superconducting disks

The magneto-elastic problem of a thin superconducting disk in a perpendicular magnetic field is analyzed with field-dependent critical current. We calculate numerically the body force distribution and discuss the field dependence of Jc on the magneto-elastic behavior during field ascent and descent for three critical state models: Bean, Kim, and exponential models. The results show that when considering a field dependence of Jc, the flux and remagnetization fronts have a larger moving speed towards the center of a disk relative to the Bean model. Simultaneously, the most dangerous stage of possible cracking for the disk will arrive early in the field decreasing stage. The magnetostriction loops are also presented during a full cycle of the applied field. It is interesting that the calculated magnetostriction loops for the Kim and exponential models are quite similar to the corresponding magnetostriction curves at low and high temperatures measured in the experiment.

Mechanical Behaviors of a Cylindrical Superconducting Composite with Transport Current

The stress, displacement, and magnetostriction induced by flux pinning for a superconducting composite cylinder, which is consisted of two concentric shells with different critical current densities, are calculated analytically in the presence of transport current. Firstly, both the flux and current distributions are given for increasing and decreasing transport current cases by adopting the Bean model. Then the elastic solutions to stress, displacement and magnetostriction are obtained by using plane strain approach. Finally, lots of numerical results on these mechanical behaviors (including the cases of inner superconducting shell being replaced by an elastomer and/or by a hole) are displayed graphically and analyzed in detail. Numerical results show that, among others, during the transport current reduction, tensile stress especially radial tensile stress will occur in the outer region of the composite, and that in general, displacement is always negative in the superconducting composite with transport current. In addition, different to homogeneous superconducting cylinder, as the applied maximal transport current exceeds outer-cylinder critical current, the hysteresis loop of the magnetostriction exists for the full cycle of the transport current. Moreover, different to superconducting composite (including the case of the inner shell being an elastomer), the inner hole has significant effects on both the stress and displacement distributions of the outer superconducting shell, and for a hollow superconductor, the magnetostriction loop still exists even if the maximal transport current does not exceeds the its critical current.

Magneto-elastic behaviour of thin type-II superconducting strip with field-dependent critical current

The magneto-elastic behavior of thin superconducting strip in perpendicular magnetic field with field-dependent critical current is studied. We calculate numerically the body force, strain, displacement, and thickness changes in the strip for the Bean model and Kim model during the field ascent and descent. The differences in magnetostriction between the Bean model and the Kim model are analyzed. The magnetostriction during one full cycle of the applied field for both models is presented. The results show that magnetostriction loops are different in these models, and at low temperatures Kim model is in better agreement with experiment than Bean model.

Angular Response of Magnetostrictive Thin Films

The magnetostrictions of the single TbFe layer and coupled Py/TbFe2 bilayers were measured by using laser deflectometry. The dependences of the magntostriction performance on the driving magnetic field direction have been investigated. The relationship studies between the saturation bending angle and torsion angle of the single layer with perpendicular anisotropy and coupled bilayers with in‐plane uniaxial anisotropy have been conducted. Interesting “jump” reflecting the spin dynamics is observed in the magnetostriction loops of the coupled bilayers.

Temperature dependent magnetostrains in polycrystalline magnetic shape memory Heusler alloys

Abstract The transformation-induced strains with and without applied magnetic field and magnetostriction loops at different temperatures have been measured for polycrystalline ferromagnetic and metamagnetic shape memory Heusler alloys such as Ni Mn Ga, Ni Fe(Co) Ga and Ni Mn Sn, respectively. The results evidence a magnetic field oriented growth of martensitic variants during the martensitic transformation in Ni Mn Ga sample, whereas this effect is not evident in the other two alloys. In the Ni Mn Sn alloy, the isotropic volume magnetostriction dominates the anisotropic domain magnetostriction.

A Dynamic Hysteresis Constitutive Relation for Giant Magnetostrictive Materials

Giant Magnetostrictive Materials (GMM), such as Terfenol-D materials, have complex nonlinear and hysteresis properties especially when the materials under pre-stresses are in a bias magnetic field and a time-varying excitation field. In order to totally describe the constitutive behavior of GMM, a static and nonlinear anhysteretic constitutive relation is analytically established by the thermodynamic theory and the theory of the Weiss molecular field. Having considered the energy loss of GMM arising from a time-varying field, such as AC magnetic field, a dynamic hysteresis constitutive relation for Terfenol-D materials is obtained in this paper. This constitutive relation can totally display the magnetic-elastic-thermal coupling properties and the effect of varied operating conditions on the minor magnetostriction loop of GMM, and are in good agreement with existing experimental data.

Temperature Dependence of Magnetostriction of ${\rm Co}_{1+x}{\rm Ge}_{x}{\rm Fe}_{2-2x}{\rm O}_{4}$ for Magnetostrictive Sensor and Actuator Applications

The temperature dependence of the magnetoelastic properties of a series of germanium/cobalt co-substituted cobalt ferrite samples has been measured. Magnetostriction loops of the compositions Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1+x</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2-2x</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> (x = 0.1 , 0.3, and 0.6) were measured over a temperature range of 250-400 K. Germanium/cobalt co-substitution was found to change the Curie temperature, anisotropy, and the magnetostriction coefficients in the crystal directions of [100] and [111]. Both magnetostriction and strain sensitivity were seen to decrease in magnitude with increasing temperature. Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.1</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.1</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.8</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> was found to have a maximum sensitivity (dlambda/dH) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sigma</sub> of 2.6 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> A <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> .m, which is twice the value obtained for pure cobalt ferrite, without any decrease in maximum magnetostriction in the linear region.

Magnetostrictive properties of Fe40Ni38Mo4B18 alloy

Magnetostrictive properties as initial curve and major and minor magnetostriction hysteresis butterfly loops of Fe 40 Ni 38 Mo 4 B 18 as-quenched amorphous alloy as a function of quasi-static magnetic field were investigated. The strip amorphous sample and semiconductor strain gauges were used. The measurements were performed in solenoid and Helmholtz coils, which enables sample to be magnetised in two perpendicular directions. Minor magnetostriction loops after each returning to zero of the magnetic field and polarised magnetostriction loops with the alternating magnetic field are shown.

Preisach modeling of magnetization and magnetostriction processes in laminated SiFe alloys

In this article, magnetization loops under mechanical stress and magnetostriction loops under quasistatic magnetic excitation conditions are discussed. In both cases, the hysteresis loops are modeled using the Preisach theory. The identification procedure of the material parameters is described. The article discusses first the shape of the Preisach distribution function for the study of magnetostriction loops. Next, a Preisach model is proposed for the description of magnetization loops under mechanical stress starting from the magnetization loop obtained without applying mechanical stress. A setup has been constructed for the measurement of magnetization loops under compressive or tensile stress. Also, a measuring system based on a single sheet tester and on optical displacement measurement techniques is used to establish the magnetostrictive behavior of laminated SiFe alloys. It is shown that a good correspondence between the calculated and measured magnetization and magnetostriction loops is obtained.